On a new subclass of bi-univalent functions satisfying subordinate conditions
Year 2019,
Volume: 68 Issue: 1, 724 - 733, 01.02.2019
Emeka Mazı
,
Sahsene Altınkaya
Abstract
The purpose of our present paper is to introduce a new subclass of bi-univalent functions associated with pseudo-starlike function with Sakaguchi type functions and to determine the coefficient estimates |a₂| and |a₃| for functions in each of this newly-defined class. We also highlight some known consequences of our main results.
References
- Altınkaya, Ş. and Yalçın, S., On a new sublass of bi-univalent functions of Sakaguchi type satisfying subordinate condition, Malaya J. Mat. 5(2), 2017, 305-309.
- Altınkaya, Ş. and Yalçın, S., Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math. 6 (2015), 180--185.
- Altınkaya, Ş. and Yalçın, S., Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces 2015 (2015), Article ID 145242, 1--5.
- Altınkaya, Ş. and Yalçın, S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Acad. Sci. Paris Sér. I 353 (2015), 1075--1080.
- Ali, R.M., Lee, S.K., Ravichandran, V. and Supramaniam, S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions. Appl. Math. Lett. 25, (2012) 344-351.
- Babalola, K.O., On λ-pseudo-starlike functions, J. Class. Anal. 3(2), (2013) 137-147.
- Brannan, D.A. and Clunie, J.G.(Eds.), Aspects of Contemporary Complex Analysis (Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1-20, 1979), Academic Press, New York and London, 1980.
- Brannan D.A. and Taha, T.S., On some classes of bi-univalent functions Studia Univ. Babe¸s-Bolyai Math, 31(2), (1986).70-77.
- Duren, P.L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York Berlin Heidelberg and Tokyo, 1983.
- Frasin, B.A., Coefficient inequalities for certain classes of Sakaguchi type functions, Int. J. Nonlinear Sci., 10(2) (2010), 206-211.
- Goyal, S.P. and Goswami, P., Certain coefficient inequalities for Sakaguchi type functions and applications to fractional derivative operator, Acta Unisarsities Apulensis (No. 1912009)
- Joshi, S. and Pawar, H., On some subclasses of bi-univalent functions associated with pseudo-starlike functions, Journal of the Egyptian Mathematical Society, 24, (2016), 522-525.
- Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coefficients of bi-subordinate functions, C. R. Acad. Sci. Paris Sér. I 354 (2016), 365--370.
- Lewin, M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc,18, (1967), 63-68.
- Murugusundaramoorthy, G., Magesh, N. and Prameela, V., Coefficient bounds for certain subclasses of bi-univalent functions, Abs. Appl. Anal., Volume 2013, Article ID 573017, 1-3.
- Netanyahu, E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Ration. Mech. Anal, 32, (1969), 100-112.
- Olatunji, S.O. and Ajai, P.T., On subclasses of bi-univalent functions of Bazilevic type involving linear and Salagean operator, Internat. J. Pure Appl. Math. 92 no.5, (2014), 645-656,
- Owa, S., Sekine, T., Yamakawa, R., On Sakaguchi type functions. Applied Mathematics and Computation, 187 (2007): 356-361.
- Sakaguchi, K., On a certain univalent mapping, J. Math. Soc. Japan, 11(1), (1959), 72-75.
- Shamugham, T.W., Ramachandran, C. and Ravichandran, V., Fetete-Szego Problem for a subclasses of starlike function with respect to symmetric points, Bull. Korean Math. Soc. 43(3) (2006), 589-598.
- Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188--1192.
- Taha, T.S., Topics in Univalent F unction Theory, Ph.D. Thesis, University of London, 1981
- Xu, Q.-H., Gui, Y.-C. and Srivastava, H. M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), 990--994.
- Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M., A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218 (2012).
- Zireh, A., Adegani, E.A. and Bulut, S., Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin 23 (2016), 487-504.
Year 2019,
Volume: 68 Issue: 1, 724 - 733, 01.02.2019
Emeka Mazı
,
Sahsene Altınkaya
References
- Altınkaya, Ş. and Yalçın, S., On a new sublass of bi-univalent functions of Sakaguchi type satisfying subordinate condition, Malaya J. Mat. 5(2), 2017, 305-309.
- Altınkaya, Ş. and Yalçın, S., Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math. 6 (2015), 180--185.
- Altınkaya, Ş. and Yalçın, S., Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces 2015 (2015), Article ID 145242, 1--5.
- Altınkaya, Ş. and Yalçın, S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Acad. Sci. Paris Sér. I 353 (2015), 1075--1080.
- Ali, R.M., Lee, S.K., Ravichandran, V. and Supramaniam, S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions. Appl. Math. Lett. 25, (2012) 344-351.
- Babalola, K.O., On λ-pseudo-starlike functions, J. Class. Anal. 3(2), (2013) 137-147.
- Brannan, D.A. and Clunie, J.G.(Eds.), Aspects of Contemporary Complex Analysis (Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1-20, 1979), Academic Press, New York and London, 1980.
- Brannan D.A. and Taha, T.S., On some classes of bi-univalent functions Studia Univ. Babe¸s-Bolyai Math, 31(2), (1986).70-77.
- Duren, P.L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York Berlin Heidelberg and Tokyo, 1983.
- Frasin, B.A., Coefficient inequalities for certain classes of Sakaguchi type functions, Int. J. Nonlinear Sci., 10(2) (2010), 206-211.
- Goyal, S.P. and Goswami, P., Certain coefficient inequalities for Sakaguchi type functions and applications to fractional derivative operator, Acta Unisarsities Apulensis (No. 1912009)
- Joshi, S. and Pawar, H., On some subclasses of bi-univalent functions associated with pseudo-starlike functions, Journal of the Egyptian Mathematical Society, 24, (2016), 522-525.
- Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coefficients of bi-subordinate functions, C. R. Acad. Sci. Paris Sér. I 354 (2016), 365--370.
- Lewin, M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc,18, (1967), 63-68.
- Murugusundaramoorthy, G., Magesh, N. and Prameela, V., Coefficient bounds for certain subclasses of bi-univalent functions, Abs. Appl. Anal., Volume 2013, Article ID 573017, 1-3.
- Netanyahu, E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Ration. Mech. Anal, 32, (1969), 100-112.
- Olatunji, S.O. and Ajai, P.T., On subclasses of bi-univalent functions of Bazilevic type involving linear and Salagean operator, Internat. J. Pure Appl. Math. 92 no.5, (2014), 645-656,
- Owa, S., Sekine, T., Yamakawa, R., On Sakaguchi type functions. Applied Mathematics and Computation, 187 (2007): 356-361.
- Sakaguchi, K., On a certain univalent mapping, J. Math. Soc. Japan, 11(1), (1959), 72-75.
- Shamugham, T.W., Ramachandran, C. and Ravichandran, V., Fetete-Szego Problem for a subclasses of starlike function with respect to symmetric points, Bull. Korean Math. Soc. 43(3) (2006), 589-598.
- Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188--1192.
- Taha, T.S., Topics in Univalent F unction Theory, Ph.D. Thesis, University of London, 1981
- Xu, Q.-H., Gui, Y.-C. and Srivastava, H. M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), 990--994.
- Xu, Q.-H., Xiao, H.-G. and Srivastava, H. M., A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218 (2012).
- Zireh, A., Adegani, E.A. and Bulut, S., Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin 23 (2016), 487-504.